,for the picture that you have re-shared here, I would like to ask something. Since displacements are already calculated from the External forces, and then we are calculating the internal forces from the resulting nodal displacements, but I don't see a reason why the internal calculated forces will not be equal to the externally applied forces. Ofcourse, this might be related to the numerical nature of the FEA softwares but where exactly it makes an approximation so that the internal forces don't become equal to the external forces (or the difference doesn't come down the defined limit). As far as a I see it, there is a straight forward way. Calculate the nodal displacements from external forces, and then re-calculate the internal forces. But why would these internal forces be different from the external forces, I couldn't grasp it.
If I am using a PCG solver, then I can assume that there might be some approximations made and internal forces are not equal to the external forces. But for a non-linear analysis where Direct solver is utilized, where no approximations are made at all (I believe) and there is a simple LU decomposition, why won't it make the internal forces become equal to the external one on the first iteration?